I've heard of that book (haven't read it yet), but when it comes to something like that it's a very personal thing and, unless she's expressed a desire to you to read it, I'd pass.
Is your friend's relative a spouse or close family member? Will she end up being a caretaker of this person? You might wait and give her the gift of time, later on - when she will need respite from her relative's illness.
My dad has terminal cancer and my stepmom is his primary caregiver. Sometimes she just needs a break. Your friend may, too.